NEET Sample Paper NEET Sample Test Paper-19

  • question_answer ) The angular velocities of three bodies in simple harmonic motion are \[{{\omega }_{1}},{{\omega }_{2}},{{\omega }_{3}}\]with respective amplitudes as\[{{A}_{1}},{{A}_{2}},{{A}_{3}}\]If all the three bodies have the same mass and maximum speeds, then:

    A) \[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\]   

    B) \[{{A}_{1}}\omega _{1}^{2}={{A}_{2}}\omega _{2}^{2}={{A}_{3}}\omega _{3}^{2}\] 

    C) \[A_{1}^{2}{{\omega }_{1}}=A_{2}^{2}{{\omega }_{2}}=A_{3}^{2}{{\omega }_{3}}\]

    D) \[A_{1}^{2}\sqrt{{{\omega }_{1}}}=A_{2}^{2}\sqrt{{{\omega }_{2}}}=A_{3}^{2}\sqrt{{{\omega }_{3}}}\] 

    Correct Answer: A

    Solution :

    \[y=A\sin \omega t\] \[v=\frac{dy}{dt}=A\omega \cos \omega t\] \[\therefore \]Maximum speed \[=A\omega \] Since all the bodies have same maximum speeds, so\[{{A}_{1}}{{\omega }_{1}}={{A}_{2}}{{\omega }_{2}}={{A}_{3}}{{\omega }_{3}}\] Hence, the correction option is [a].

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